1. Field of the Invention
The present invention is related to the field of signal processing methods for oil well logging tools. More specifically, the present invention is related to signal processing methods for reducing noise in signal data comprising exponentially decaying signal components, in particular, spin echo decay signals from nuclear magnetic resonance (NMR) well logging instruments.
2. Description of the Related Art
Oil well logging tools include nuclear magnetic resonance (NMR) instruments. NMR instruments can be used for determining, among other things, the fractional volume of pore space and the fractional volume of mobile fluid filling the pore space of earth formations. Methods of using NMR measurements for determining the fractional volume of pore space and the fractional volume of mobile fluids are described, for example, in "Spin Echo Magnetic Resonance Logging: Porosity and Free Fluid Index Determination", M. N. Miller et al, Society of Petroleum Engineers paper no. 20561, Richardson, Tex., 1990.
NMR instruments known in the art are typically designed to make measurements corresponding to an amount of time for hydrogen nuclei present in the earth formation to realign their spin axes, and consequently their bulk magnetization, either with an externally applied magnetic field, or perpendicularly to the magnetic field, after momentary reorientation of the nuclear spin axes. The externally applied magnetic field is typically provided by a magnet disposed in the NMR instrument. The spin axes of the hydrogen nuclei in the earth formation are, in the aggregate, caused to be aligned with the magnetic field induced in the earth formation by the magnet. The NMR instrument includes an antenna positioned near the magnet and shaped so that a pulse of radio frequency (RF) power conducted through the antenna induces a magnetic field in the earth formation orthogonal to the field induced by the magnet. The RF pulse has a duration predetermined so that the spin axes of the hydrogen nuclei generally align themselves perpendicular both to the orthogonal magnetic field induced by the RF pulse and to the externally applied magnetic field. After the pulse ends, the nuclear magnetic moment of the hydrogen nuclei gradually "relax" or return to their alignment with the externally applied magnetic field. The amount of time taken for this relaxation is related to properties of interest of the earth formation.
After the RF pulse ends, the antenna is typically electrically connected to a receiver, which detects and measures voltages induced in the antenna by precessional rotation of the spin axes of the hydrogen nuclei. While the hydrogen nuclei gradually realign their spin axes with the magnet's field, they do so at different rates because of inhomogeneities in the magnet's field and because of differences in the chemical and magnetic environment within the earth formation. Different rates of realignment of the spin axes of the hydrogen nuclei results in a rapid decrease in the voltage induced in the antenna. The rapid decrease in the induced voltage is referred to as the free induction decay (FID).
After a predetermined time period following the FID, another, longer RF pulse is applied to the antenna. The longer RF pulse has a duration predetermined to realign the spin axes of the hydrogen nuclei in the earth formation by an axial rotation of 180 degrees from their immediately previous orientations. After the longer RF pulse (called a 180 degree pulse), hydrogen nuclear axes that were realigning with the externally applied field at a slower rate are then positioned so that they are "ahead" of the faster realigning spin axes. The 180 degree movement causes the faster realigning axes are reoriented to be "behind" the slower realigning axes. The faster realigning axes eventually "catch up" to, and come into approximate alignment with, the slower aligning axes after the 180 degree reorientation. As a large number of the spin axes become aligned with each other, the hydrogen nuclei again are able to induce measurable voltages in the antenna. The voltage induced as a result of realignment of the hydrogen nuclear axes with each other after a 180 degree pulse is referred to as a "spin echo". The spin echo induced voltage is smaller than the original FID voltage generated after cessation of the first RF pulse, because the aggregate nuclear axial alignment, and consequently the bulk magnetization, of the hydrogen nuclei at the time of the spin echo is at least partially realigned with the magnet's field and away from the sensitive axis of the antenna. The spin echo voltage itself rapidly decays by FID as the faster aligning nuclear axes "dephase" from the slower aligning nuclear axes.
After another period of time equal to two of the predetermined time periods between the initial 90 degree RF pulse and the first 180 degree pulse, another RF pulse, of the same duration as the pulse causing the 180 degree shift in spin axis orientation, can be applied to the antenna. This next 180 degree pulse again causes the slower realigning spin axes to be positioned ahead of the faster realigning axes, and eventually another spin echo will induce voltages in the antenna. The induced voltages of this next spin echo will typically be smaller in amplitude than the previous spin echo.
Successive 180 degree RF pulses are applied to the antenna to generate successive spin echoes, each one typically having a smaller amplitude than the previous spin echo. The rate at which the peak amplitude of the spin echoes decays is related to properties of interest of the earth formation, such as the fractional volume of pore space or the fractional volume of mobile fluid filling the pore space. The number of spin echoes needed to determine the rate of spin echo amplitude decay is related to the properties of the earth formation; in some cases as many as 1,000 spin echoes may be needed to determine the amplitude decay corresponding to the properties of the earth formation which are of interest.
When any of the RF pulses are applied to the antenna, the magnet can become physically deformed by magnetostriction. After each RF pulse is turned off, the magnet tends to return to its original shape in a series of damped mechanical oscillations, known as "ringing". Ringing induces large voltages in the antenna which can interfere with measurement of the voltages induced by the spin echoes.
A method known in the art for reducing the effect of ring-induced voltages is to make spin echo measurements in cycles known as "phase alternate pairs" (PAPS). PAPS measurements are performed by making a second set of spin echo measurements starting with an original transverse alignment (90 degree) RF pulse which is inverted in phase from the 90 degree pulse used to start the first set of spin echo measurements. Voltages induced in the antenna during the second set of spin echo measurements will be inverted in polarity from the voltages induced in the first set of measurements. The voltages from the second set of measurements can be subtracted from the voltages in the first set of measurements to substantially remove coherent noise such as the ring-induced voltages.
In order to correctly subtract the second set of voltage measurements from the first set of voltage measurements, the spin echoes from the first set and the second set must be substantially time correspondent. Small time differences between successive sets of measurements can result from variations in phase response of the antenna and of analog amplifier circuits forming part of the receiver to which the antenna is connected. The amplitude of each one of the spin echoes is typically measured by connecting the receiver to a phase sensitive detector. The phase sensitive detector measures only a voltage amplitude component having a predetermined phase relationship with respect to a phase reference. In the typical NMR instrument, the phase reference can be an oscillator which generates the RF voltages used to apply the RF pulses to the antenna. Differences in phase response of the antenna and analog amplifier circuits can be adjusted by referencing the phase sensitive detector to the oscillator.
It is known in the art to improve the signal-to-noise ratio of NMR well logging measurements by averaging a plurality of PAPS, typically eight or more.
A drawback to using phase sensitive detectors is that the signal phase must be measured precisely or the signal phase must remain constant over the duration of the measurement. The signal phase is typically not constant for the duration of the measurement because of tool motion. In addition, measurement system noise, which can include thermal noise in the dectronic circuits forming the receiver, can be of sufficient amplitude to cause the phase measurements to be imprecise. In the NMR instruments known in the art, the voltage signal is rectified after phase alternate pairs are combined. Later in a spin echo measurement cycle, as the voltages induced by the spin echoes are greatly reduced in amplitude, noise in the measurement system, which can include thermal noise in the electronic circuits forming the receiver, can be of sufficient amplitude to cause absolute signal level excursions which change the polarity of the measured voltage. The detection scheme known in the art rectifies the opposite polarity voltage excursions, and the resulting spin echo amplitude signal can include apparent decay rates not representative of the properties of the earth formation.
Accordingly, it is an object of the present invention to provide a method of filtering spin echo measurement signals which reduces the effect of rectified noise in the receiver circuitry in an NMR logging instrument.